Computer simulation of logarithmic transformation function to expand the range of high-precision measurements

Abstract

Studies of the effect of normalized radiation fluxes on the measurement result revealed the most influential one. The value of the normalized flow F0 was shown to have a greater effect on the relative measurement error than ΔF0. This allows investigating the relationship between the controlled Fx and the normalized flow F0. Experimental studies have confirmed that by a threefold increase in the normalized flow F0 relative to the controlled flow Fx, it becomes possible to increase the measurement accuracy in a wide range. In particular, it was found that at the flux value F0=0.16×10-3 W, it becomes possible to measure the controlled flow in a wider range Fх=(0.16×10-3÷0.97×10-3) W with a relative error of thousandths of a percent. The effect of the reproduction error on the measurement result under the condition of a threefold increase in the normalized flow F0 relative to the controlled flow Fх is shown. It was found that an increase in the reproduction error of the normalized radiation fluxes by 1 order leads to a narrowing of the range in which the value of the relative error tends to zero. It is shown that in the absence of a threefold increase in the normalized flow F0, an increase in the reproduction error of the normalized flows by 1 order leads to individual cases of reduction in the relative error to small-order values. The latter, by the way, applies to cases where the ratio between the normalized F0 and controlled flow Fx, as 3 to 1, is ensured. It is shown that the reproduction error of the dark flow does not affect the measurement result.Thus, there is reason to believe that it is possible to expand the measurement range, in which the value of the relative error is thousandths of a percent, even for 1 measurement cycle

Determining features in the application of redundancy for the thermistor cubic transformation function using computer simulation

“…A study was conducted to determine the influence of values of normalized values T 0 and ∆T on the measurement result over the entire range of measured temperatures T x . This does not differ from the approaches that were reported in [20], in which regularities between normalized and sought values were also taken into account. As a result, it was established (Table 1) that the value of the relative error decreases when the value of the normalized temperature T 0 increases and remains constant when the values of the normalized temperature ∆T change.…”

“…This circumstance is due to the fact that in order to introduce redundancy, it is necessary to form value-normalized physical quantities of the same physical nature as the measuring one. Therefore, in work [20] regularities between normalized and sought values were established, which leads to the expansion of the range of high-precision measurements. The expediency of using redundant methods is also confirmed by their application with a quadratic sensor transformation function [21].…”

Computer modeling in the study of the effect of normalized quantities on the measurement accuracy of the quadratic transformation function

“…Processing of measurement results in accordance with the proposed equations provides automatic exclusion of the additive and multiplicative components of the error, i.e. error correction, which does not contradict the data presented in [19][20][21][22][23][24][25]. In addition, due to the application of the proposed redundant measurement equations ( 11) and ( 14), it is possible to directly use a nonlinear TF without special measures for its linearization, which are typical for studies published in [12][13][14].…”

“…However, the issue of the influence of the values of normalized quantities and their relationship with the desired quantity on the final measurement result for a nonlinear transformation function remains unresolved. Therefore, further research on redundant measurement methods presented in [25] established a relationship between the normalized and desired quantities, which significantly expands the range of high-precision measurements. The results obtained demonstrated the high efficiency of redundant measurement methods in improving measurement accuracy by adjusting the values of normalized quantities for the logarithmic transformation function.…”

Computer analysis of multiple measurements with the sensor's quadratic transformation function

“…It is shown that this allows increasing the accuracy of measurements by eliminating the systematic component of the error due to changes in the parameters of the transformation function, as well as reducing the random component of the error. Redundant measurements with a nonlinear transformation function were further developed in [19]. It is shown that due to the regularity between the normalized and sought quantities, the range of high-precision measurements is significantly expanded.…”